1. Field of the Invention
The present invention relates to photolithography, and more particularly to a method for designing an illumination light source of an exposure tool, a method for designing a mask pattern, a method for manufacturing a photomask, a method for manufacturing a semiconductor device, and a computer program product for designing an illumination light source.
2. Description of the Related Art
In an exposure process for manufacturing a semiconductor device, a mask pattern drawn on a photomask is transferred onto a resist film deposited on a semiconductor substrate. In an exposure tool that transfers the mask pattern, a light emitted from an effective light source illuminates the photomask. The illumination light transmitted and diffracted from the photomask is collected on the resist film by a projection lens to form an optical image. The resist film is sensitized by the formed optical image. The exposed semiconductor substrate is developed to form a resist pattern.
Errors induced by the exposure tool may cause a dimensional variation in the resist pattern from a desired value. For example, the induced errors may include an error of an exposure dose, an error of a height of the substrate with respect to a lens, i.e., a focus error, and the like. Based on a variation tolerance of a dimension of the resist pattern, it is possible to determine the accuracy of an exposure dose and a focus, which are required for the exposure tool. The accuracy of an exposure dose and a focus are respectively referred to as an exposure latitude and a depth of focus.
Image capability of an exposure tool for a fine pattern is represented by the following Rayleigh equation:R=k1×λ/NA   (1)Here, R is the resolution of the exposure tool expressed in term of the smallest resolvable half-pitch that is one half of a minimum period of a periodic pattern. λ is a wavelength of an exposure light. NA is a projection side numerical aperture of a projection lens of the exposure tool. k1 is a factor that indicates efficiency of a photolithography process.
When the k1 factor is lower, i.e., when a finer mask pattern is exposed without changing the wavelength λ of the exposure light and the numerical aperture NA of the projection lens, an exposure latitude and a depth of focus for the mask pattern are decreased. Thus, a dimension of a transferred resist pattern may easily vary outside the range of a variation tolerance. Therefore, a higher transfer accuracy is required for the exposure tool.
To solve such problem, a method for increasing an exposure latitude and a depth of focus for a mask pattern by using a modified illumination has been proposed. Japanese Patent Laid-Open No. S61-91662 discloses an illumination method in which a light intensity of a periphery of an effective light source is larger than a center portion thereof. By use of the modified illumination such as an annular illumination and a quadrupole illumination, the exposure latitude and depth of focus for a fine mask pattern can be increased.
However, when the mask pattern is further miniaturized, even by using the annular illumination or the quadrupole illumination, it may be impossible to ensure a sufficient exposure latitude and a sufficient depth of focus for the mask pattern. Additionally, when a variety of features of mask patterns having different dimensions are provided in the photomask, it is not easy to determine which type of modified illumination is better to use. A method to select an optimal illumination, from among a plurality of illuminations, by trial and error is generally implemented by calculating an exposure latitude and a depth of focus. However, the method to select an optimal illumination necessitates a great amount of time and effort.
In order to optimize a shape of an illumination aperture, a proposal has been disclosed, in which an effective light source is divided into a plurality of minute areas, and a normalized image log-scale (NILS) at each of the best focus and defocus of a light intensity distribution is used as an index (see Japanese Patent Laid-Open No. P2004-128108). The normalized image log-scale is defined as a slope of the logarithm of an optical image. Additionally, there has been disclosed a method in which an effective light source is divided in a grid pattern to calculate a light intensity of a lattice point on a semiconductor substrate for each grid of the effective light source, and to optimize a shape of an illumination aperture based on a dispersity of the light intensity (see Japanese Patent Laid-Open No. P2004-79714).
Furthermore, when a pattern dimension is less than the wavelength of an illumination light, a dimensional variation of an image, depending on a polarization state of the illumination light, increases. When a light enters a surface of a semiconductor substrate, a vibration direction of an electric field vector may be perpendicular to the plane of incidence (S-polarization), or parallel to the plane of incidence (P-polarization).
The vibration directions of the electric field vectors of the P-polarized lights that interfere with each other are not parallel to each other. The vibration directions of the electric field vectors of the S-polarized lights that interfere with each other are parallel to each other. Thus, an image contrast of the P-polarization deteriorates as compared with the S-polarization. The image contrast deterioration increases as a mask pattern becomes finer. Accordingly, by applying an S-polarized light, the image contrast is improved, and exposure latitude is increased. As a result, a variation of a resist dimension may decrease.
However, in an actual photomask for semiconductor device manufacturing, mask patterns are arranged in different directions. Thus, it is not easy to determine which polarized light is used to illuminate the mask patterns.